PONDEROMOTIVE ION ACCELERATION AND FAST ION IGNITION WITH ULTRAINTENSE LASER PULSES

Transcription

1 PONDEROMOTIVE ION ACCELERATION AND FAST ION IGNITION WITH ULTRAINTENSE LASER PULSES V.Tikhonchuk Centre Lasers Intenses et Applications Université Bordeaux 1, France Senigallia, June 15, 2009 COULOMB 09 Ions Acceleration with High Power Laser: Physics and Applications 1

2 Co-authors N. Naumova Laboratoire d'optique Appliquée, ENSTA, Palaiseau, France T. Schlegel GSI, Darmstadt, Germany I. V. Sokolov Space Physics Research Laboratory, University of Michigan, USA C. Labaune Laboratoire d Utilisation Lasers Iintenses, Ecole Polytechnique, France G. Mourou Institut de la Lumière Extrême, France C. Regan, J.-L. Feugeas, Ph. Nicolaï, X. Ribeyre, G. Schurtz Centre Lasers Intenses et Applications, Université Bordeaux 1, France M. Temporal ETSIA, Universidad Politécnica, Madrid, Spain Ion acceleration and fast ignition, Senigallia, June 15,

3 Outline Ion acceleration by the radiation pressure: the laser piston quasi-stationary model Numerical simulations of the high-intensity ion acceleration and hole boring Effect of the electron radiation losses on the ion acceleration Fast ignition with ponderomotively accelerated ions Ion acceleration and fast ignition, Senigallia, June 15,

4 Ion acceleration with high intensity laser pulses Fast ions can find many applications in fusion, industry and medicine: low ratio current/energy flux, simple ballistic transport, high absorption efficiency ( 2 ρl ) 0.56 εi 45 / g/cm MeV but one needs an efficient and compact ion accelerator to the energies > MeV. Two mechanisms of laser ion acceleration have been considered: TNSA target normal sheath acceleration from a narrow layer at the rear side requires an efficient production of high energy electrons, high quality target surface, less restrictions on the laser pulse, limited number of ions ponderomotive acceleration in the volume of target requires cold electrons, high quality laser pulse, less restrictions on the target, could be more efficient, more ions could be accelerated Ion acceleration and fast ignition, Senigallia, June 15,

5 Ion acceleration by the laser piston: the piston velocity Conservation of the momentum (pressure) in the piston reference frame: stationary propagation I c 1 β las f β f = ργ β c f f piston velocity v f = β f c β f = I las I + las ρc 3 laser ion energy and the efficiency of ion acceleration are defined by the piston velocity charge separation layer ε = 2mc βγ i i f f 2β f 1 R = 1 + β Naumova et al., PRL, 102, 2009, Robinson et al., PPCF, 51, 2009 Ion acceleration and fast ignition, Senigallia, June 15, f

6 Structure of the charge separation layer: electrostatic field and ion density distribution The electrostatic field profile in the charge separation layer follows from the Poisson equation (n e = 0) 2 ' d Φ '2 = dz ' Z en i ε 0 and the ion energy and mass conservation in the piston reference frame: ( ) ZeΦ+ ε = m c γ 1; n = 2n γ ' ' 2 ' f i i f i 0 f ' vi v n i E z ε i The first integral defines the electric field strength: 2n 0 ' dγ ω i pi = 2 βγ 1 ' f f i dz c ( '2 γ ) 1/4 1 β f z max las 1+ β f Ion acceleration and fast ignition, Senigallia, June 15, E z a ~v f /ω pi 2E 0 z

7 Thickness of the ion charge separation layer The thickness of the ion charge separation layer is proportional to the piston velocity (if β f «1) Δz 0 0 The time of ion circulation is independent on the laser intensity i acn 0 3ω n Δt 2γ ω c i f pi This time of ion circulation coincides exactly with the period of piston velocity oscillations found in the PIC simulations E z,max E x,max a 0 = 20, n 0 = 20n c a 0 = 100, n 0 = 20n c t /T t /T Ion acceleration and fast ignition, Senigallia, June 15,

8 Structure of the charge separation layer: laser field and electron density distribution The electrostatic field profile in the charge separation layer follows from the Poisson equation 2 ' d Φ e '2 = dz ' Zni n ε 0 ' e and the electron energy and mass conservation in the piston reference frame: ( ) Φ+ e ε = m c γ 1; n = 2Zn γ ' ' 2 ' f e e f e 0 f ' ve 2 ' ' ' d γe n 0 Zγe γ i = 2γ 2 fβ f dζ n '2 2 '2 c γe 1 a γi 1 n Zβ a 1 β f = 1 + β 2 da 0 f 2γ 2 f dζ n '2 '2 c γ e 1 a The electron layer thickness c/ω pe the laser field f a v a E z da dζ n e 2 ζ = 0 + a ε e 2n 0 0 c/ω pe 4a 2 2 ζ = β 1+ β f f z Ion acceleration and fast ignition, Senigallia, June 15,

9 Laser amplitude in the electron charge separation layer Laser amplitude on the board of the electron charge separation layer a(0) is adjusted self-consistently in such a way that the ponderomotive force is equal to the electric force: F pf = e E zmax It decreases slowly with the plasma density a a(0) E z n e ε e 2n 0 0 c/ω pe z A very tight balance between the ponderomotive potential and the electrostatic field can make the electron confinement unstable Ion acceleration and fast ignition, Senigallia, June 15,

10 Electron radiation and slowing down Thomson scattering is strongly amplified in the relativistic laser field due to the high order harmonic generation: if γ e << a if γ e >> a ω max e ω ωa P a rad 6πε 0c Radiation is enhanced if the electron propagates toward the laser beam with a high energy, γ e >> a >> 1. The photons with the frequencies ω ph ~ ω a γ e2 are emitted in a narrow cone θ ~ a/γ e << 1. The electron radiation stopping length l c 1 1 λ rad reω γ ea 40 rea nc n 2e ω ω 4ωaγ P γ a 3 5 μm for n 0 /n c = 40, a = 100 electrons are confined behind the piston e rad e 3πε 0c Radiation losses can be significant for laser amplitudes a > 100 and for linear polarization Ion acceleration and fast ignition, Senigallia, June 15, max Esarey et al., Phys. Rev. E 48, 1993 a 0 = 100 n 0 = 10n c

11 Ion energy spectrum in inhomogeneous plasma Ions are mono-energetic in a homogeneous plasma, in an exponential density profile the ions are a power spectrum Deuteron spectra in a plasma with the density increasing from 1 to 100n c dni I L 1 = dε 2m c β γ 1 β las i f f f ( + ) f min f max Ion acceleration and fast ignition, Senigallia, June 15, ε i 4I = n las imax c ln β β

12 Time of hole boring and laser fluence Analytical formulas provide the scalings for design of the fast ignition parameters, 10 GJ/cm 2 F 100 = I inc T p is the laser flux needed for accelerate ions from the density increasing from 1 to 100n c over the length of 100λ, F 1 is the same for the density range 0.1 to 1n c over the length of 1000λ T p mc i = I las Ldn n i i F las = mci i las L n d i n i F Lε ( n )dn i i i i Ion acceleration and fast ignition, Senigallia, June 15,

13 1D & 2D PIC simulations of ion acceleration & hole boring Series of 1D simulations was dedicated to validation of the ion acceleration model in homogeneous and inhomogeneous plasmas 2D simulations in a plasma with exponential profile were dedicated to the analysis of the ion energy distribution and divergence in function of the laser intensity distribution Laser pulse: a 0 = 100 circularly polarized I 0 = W/cm 2 τ = 188 λ/c 2D: d/λ = 20 flat-top with exp. wings Plasma: deuterium exponential profile L/λ = 20 n 0 /n c = laser 5n c 100n c Ion acceleration and fast ignition, Senigallia, June 15, z/λ

14 Numerical modeling of the electron radiation losses The code accounts for the electron radiation in the laser field and for the electron slowing down due to the radiation emission I.V. Sokolov, Re-normalization in the Lorentz-Abraham-Dirac equation for radiation force in classical electrodynamics, JETP 108 (2009) I.V. Sokolov, N.M. Naumova, J.A. Nees, G.A. Mourou, V.P.Yanovsky, Dynamics of Emitting Electrons in Strong Electromagnetic Fields, arxiv: The electron motion is described by the modified Lorentz-Abraham-Dirac equation, which conserves electron energy and momentum dp v dx = f eδ v B P = v + δ v dt c dt e e e L e 2 rad e e 2 ( ) P f = e E+ v B = γ δv f L e rad e e L The emission of each electron is supposed to be incoherent, its motion is approximated by a fraction of a circle at each time step, assuming δv e << v e ( ) ( v f ) f v v f / c 2 δv τ ω p f p 2 2 τ 0 L e e L e 2 e = 2 0 = = / 3 rot e L e me 1 + τ 0 e L / mec 3mec Ion acceleration and fast ignition, Senigallia, June 15,

15 Example of 1D PIC simulation a 0 = 20, I 0 = W/cm 2 n 0 = 20 n c P z,e /m e c Estimates: 1 R = β f = 0.07 T b = 93T ee z /m e ω o c= 37 p i /m i c = 0.14 ε i = 18 MeV 0.2% E z,max P z,i /m i c t / T P z,i /m i c 12.8% z /λ z /λ dn/dε i Ion acceleration and fast ignition, Senigallia, June 15, ε i MeV

16 1D PIC simulations with/without radiation reaction a 0 = 100, circular polarization, t = 200T, plasma: n 0 = 10n c, m i = 2m p radiation losses : 43% without radiation losses P z,i /m i c P z,e /m e c 5.7% 31.4% P z,i /m i c P z,e /m e c z /λ z /λ Electrons escape the ponderomotive potential if the ratio a 0 /(n 0 /n c ) becomes too large. The radiation losses stabilize the piston Ion acceleration and fast ignition, Senigallia, June 15,

17 2D PIC simulation channel formation t = 90λ/c Flat-top laser intensity profile ions Ion density distribution demonstrates an efficient hole boring in the plasma, a clean and a stable channel Filamentation is strongly suppressed due to radiation pressure and radiation losses Velocity of hole boring is in agreement with the 1D model y/λ y/λ t = 190λ/c ions z/λ Ion acceleration and fast ignition, Senigallia, June 15,

18 2D PIC simulation ion energy distribution and angular spread Angular distribution of ions vs energy at the final instant at y/λ < 10 shows a narrow peak in forward direction Energy distribution in the central part (a cone of 6 o ) agrees well with 1D PIC simulations and analytical model laser Ion acceleration and fast ignition, Senigallia, June 15,

19 Design of the ion acceleration parameters for the FI The ignition proceeds in two stages (M. Tabak et al. Phys. Plasmas, 1994): 1st pulse hole boring 2 nd pulse ion acceleration Compressed target Ion acceleration and fast ignition, Senigallia, June 15,

20 Design of the ion acceleration parameters for the FI The ignition proceeds in two stages (M. Tabak et al. Phys. Plasmas, 1994): 1st pulse hole boring 2 nd pulse ion acceleration Pulse 1 hole boring Ion acceleration and fast ignition, Senigallia, June 15,

21 Design of the ion acceleration parameters for the FI The ignition proceeds in two stages (M. Tabak et al. Phys. Plasmas, 1994): 1st pulse hole boring 2 nd pulse ion acceleration Pulse 2 Ion acceleration Ion acceleration and fast ignition, Senigallia, June 15,

22 Design of the ion acceleration parameters for the FI The ignition proceeds in two stages (M. Tabak et al. Phys. Plasmas, 1994): 1st pulse hole boring 2 nd pulse ion acceleration Ion propagation and energy deposition Ion acceleration and fast ignition, Senigallia, June 15,

23 Conditions for the fast Ignition: isochoric heating Ignition conditions of a compressed sphere of DT fuel are defined by the core density ρ S.Atzeni, Phys.Plasmas, 6, 1999 E r τ ign ign ign g/cm 18 kj ρ g/cm 20 μm ρ g/cm 21 ps ρ g/cm < ρ < 500g/cm 3 r ign ε i Eign Vi, EL R ρ, ρ R ( 2 ρl ) / g/cm MeV deuteron stopping power: ε i ~ 10 MeV number of ions ~ Ion acceleration and fast ignition, Senigallia, June 15,

24 Design of ion acceleration parameters The key parameters for the fast ignition are the energy flux and the ion average energy are defined by the shell density and the shell areal density The shell areal density defines the average ion energy, while the ion fluence is defined by the the shell density Τ ρ HiPER baseline target at the stagnation time: ρ max = 600 g/cc ρl = 0.6 g/cm 2 F i 2GJ/cm 2 ε i 30 MeV CHIC simulation for the HiPER baseline target, stagnation time Ion acceleration and fast ignition, Senigallia, June 15,

25 Design of laser and plasma parameters for the fast ignition The plasma density profile is taken at the stagnation phase: HiPER baseline target ρ( r) = 4.3(g/cc)exp L = 15μm r b = r 100μm 15μm 15μm Zone of ion acceleration 6 mg/cm 2 30 µm Laser pulse duration T 2 L ρ c/ I 3ps p max las The theoretical formulas for the ion flux and energy define the laser intensity and plasma density in the acceleration zone ρ I ε max i = 2 ρ Fi = IlasLln c ρ 2 i m I c las ln ( ρ ρ ) ρ max max max min 22 2 las 10 W/cm a = 65 ρ min min = 4g/cm ρ 0.5g/cm 3 3 min Ion acceleration and fast ignition, Senigallia, June 15,

26 Ion injection & energy deposition: HiPER beaseline tgt Module of the ion ballistic transport through the inhomogeneous plasma Injection of the DT ions with the divergence of 6 from the zone g/cc ρl ions = 5 mg/cm 2 ρl shell = 600 mg/cm 2 ε i = 5 20 MeV The injected ion energy is 28 kj, the ion fluence is 1.5 GJ/cm 2, the ion temperature is 8 kev, and the absorption efficiency is ~ 73% Ion acceleration and fast ignition, Senigallia, June 15,

27 Ignition and combustion: integrated CHIC simulation Ignition occurs 20 ps after ion injection: it is due to the shock collision with the opposite part of the shell Energy of 8.5 MJ is released The laser power is 150 PW, the laser energy is 200 kj, and the conversion efficiency is ~ 10% Estimated gain ~ 20 The HiPER baseline target is not well adapted for fast ignition Ion acceleration and fast ignition, Senigallia, June 15,

28 Ignition of a large areal mass targets Targets with a larger amount of fuel can be easier ignited but they require more energy for compression Two examples of targets with large areal mass ~ 2 g/cm 2 : DUED simulations Red: Clark & Tabak, Nucl. Fus. 37, 2007 Mass 0.9 mg; ρ max = 450 g/cc Compression energy 500 kj Ion ignition energy 17 kj Fusion yield 90 MJ Blue: Temporal et al Phys.Plasmas 9, 2002 Mass 3.5 mg; ρ max = 650 g/cc Compression energy 1 MJ Ion ignition energy 12.7 kj Fusion yield 200 MJ Laser power 30 PW, energy 100 kj Ion acceleration and fast ignition, Senigallia, June 15,

29 Combustion in the targets with large ρr temperature Targets with large ρr can be ignited directly in the ion energy deposition region: less losses on the rarefaction wave density Ion acceleration and fast ignition, Senigallia, June 15,

30 Conclusions Laser acceleration of ions by the ponderomotive pressure could be efficient at high intensities: high contrast and circular polarization are needed A model of a laser piston predicts the ion energy spectrum in function of the laser and plasma parameters. Numerical simulations are in a good agreement with the model: suppression of laser beam filamentation in the channel, stabilizing effect of electron radiation losses on the channel formation More extended 2D simulations are under way. The main issues are: ion energy spectrum, stability of ion acceleration, ion beam divergence, electron radiation losses Hydro simulation are showing a possibility of the fuel ignition at the 30 PW & 100 kj level: a simple shell target adopted for the reactor. Possible optimization by using lower intensities and higher Z ions Hole boring in the underdense plasma could be a serious problem. Different physics for under- and over-dense plasmas. Multiple consecutive pulses could be an option, role of fast electrons Ion acceleration and fast ignition, Senigallia, June 15,